To find the mole fraction of urea (often referred to by the placeholder name "wren" here) and water in a solution that is 6% urea by mass, we'll walk through the steps systematically.
### Step 1: Determine the masses of urea and water
Assume we have 100 grams of the solution. Since the solution consists of 6% urea by mass, the mass of urea in the solution can be calculated as follows:
- Mass of urea = [tex]\(0.06 \times 100 \text{ g} = 6.0 \text{ g}\)[/tex]
The remaining mass is water:
- Mass of water = [tex]\(100 \text{ g} - 6.0 \text{ g} = 94.0 \text{ g}\)[/tex]
### Step 2: Calculate the moles of urea and water
Next, we need to calculate the moles of each component using their molar masses.
The molar mass of urea (CO(NH[tex]\(_2\)[/tex])[tex]\(_2\)[/tex]) is approximately 60.06 g/mol. Therefore, the moles of urea are:
- Moles of urea = [tex]\(\frac{6.0 \text{ g}}{60.06 \text{ g/mol}} \approx 0.0999 \text{ mol}\)[/tex]
The molar mass of water (H[tex]\(_2\)[/tex]O) is approximately 18.015 g/mol. Therefore, the moles of water are:
- Moles of water = [tex]\(\frac{94.0 \text{ g}}{18.015 \text{ g/mol}} \approx 5.2179 \text{ mol}\)[/tex]
### Step 3: Calculate the total number of moles in the solution
Now, add the moles of urea and water to find the total number of moles in the solution:
- Total moles = [tex]\(0.0999 \text{ mol} + 5.2179 \text{ mol} \approx 5.3178 \text{ mol}\)[/tex]
### Step 4: Determine the mole fraction of each component
The mole fraction of a component is the ratio of the moles of that component to the total moles in the solution.
For urea (wren):
- Mole fraction of urea = [tex]\(\frac{\text{moles of urea}}{\text{total moles}} = \frac{0.0999 \text{ mol}}{5.3178 \text{ mol}} \approx 0.0188\)[/tex]
For water:
- Mole fraction of water = [tex]\(\frac{\text{moles of water}}{\text{total moles}} = \frac{5.2179 \text{ mol}}{5.3178 \text{ mol}} \approx 0.9812\)[/tex]
### Conclusion
The mole fraction of urea in the solution is approximately 0.0188, and the mole fraction of water is approximately 0.9812.
